Chloe has already read 50 pages of a book and reads 40 additional pages per hour. Write the equation of the line that represents the number of pages read y in x hours. Plus sign Minus sign Multiplication sign Division sign Big fraction Superscript (Ctrl+Up) Square root Root Equals sign Not equal to Less-than sign Greater-than sign Less-than or equal to Greater-than or equal to Parentheses Pi

Answer:

8b

Step-by-step explanation:

You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:

\(\displaystyle{16b-8b=\left(16-8\right)b}\)

Then evaluate and simplify:

\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)

Answer:

Step-by-step explanation:

A = {2,8,10,14}

B= {6,8,20}

C={8,18,20,24}

A ∩ B --> intersection means elements that  are in both sets A & B

A ∩ B = {8}

A∩ C =  {8}

B ∩ C = {8 , 20}

A∩B ∩ C = {8}

First blue box = { 2,10, 14}

Second blue box = {18, 24}

First green box = { 8}

Second green box = { 20}

b) A ∩ B = {8}

n [ A ∩ B] = 1

Probability of the number to be a member of A∩B =  1 / 25

\(1.58×10^−6 g\) is equivalent to 1.58 mg.

To convert grams to milligrams, we need to multiply the given value by a conversion factor. Since there are 1,000 milligrams in 1 gram, we can multiply the given value by 1,000 to convert it to milligrams.

Given:\(1.58×10^−6 g\)

To convert to milligrams:

\(1.58×10^−6 g × 1,000 mg/g = 1.58 mg\)

Therefore,\(1.58×10^−6 g\) is equivalent to 1.58 mg.

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Answer:

432

Step-by-step explanation:

72 x 6 = 432

you are multiplying the packages x the cookies in each one

Answer:

1.5

Step-by-step explanation:

Answer:

the answer is 6/10, 5/8, 2/3

Step-by-step explanation:

we find that the graph intersects the x-axis at x = -6, x = -3, and x = -9. The zeros of the function f(x) = x^3 + 27x^2 + 268x + 954 are -6, -3, and -9.

To find the zeros of the function, we need to solve the equation f(x) = 0. However, given the degree of the polynomial, finding the zeros algebraically can be challenging. In such cases, it is helpful to use a graphing utility to visualize the function and determine its zeros.

By graphing the function f(x) = x^3 + 27x^2 + 268x + 954, we can observe the x-values at which the graph intersects the x-axis. These x-values correspond to the zeros of the function.

Using a graphing utility or software, we find that the graph intersects the x-axis at x = -6, x = -3, and x = -9. Therefore, these are the zeros of the function f(x).

Hence, the zeros of the function f(x) = x^3 + 27x^2 + 268x + 954 are -6, -3, and -9.

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The height of cone is 10 inches.

What is cone?
A cone is indeed a three-dimensional geometric shape with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex. A cone is made up of a collection of line segments, half-lines, as well as lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex. The base may only be a circle, any closed one-dimensional figure, any one-dimensional quadratic shape in the plane, or any combination of the above and furthermore all the enclosed points, depending on the author.

What is the formula for finding the height of a cone?

We know that

If two figures are similar, then the ratio of its corresponding sides is proportional

Let x----> the height of cone B

using proportionality

3/2 = 15/x

x = 2 * 15/3

x = 10 inches

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Answer:10.4

Step-by-step explanation:

There are a lot of information's that are already given in the question. Based on these information's the answer can be deduced.

1 mile = 1609 meters

Then

70 miles = 1609 * 70 meters

              = 112630 meters

again

1 hour = 3600 seconds

3 hours = 3600 * 3 seconds

            = 10800 seconds

So

Speed = 112630/10800 meters/second

          = 10.4 meters per second.

So the falcon was flying at a speed of 10.4 meters per second.

Answer:

I assume that we want to complete the statement:

"The maximum profit of $__ dollars is reached when __ items are produced"

We know that the profit equation is defined between x = 0 and x = 100, which are the two roots of the equation (so the profit is equal to zero for x = 0 and for x = 100).

Then we can assume that the profit will be positive in this range.

Thus, the quadratic equation should have a negative leading coefficient, which would mean that the arms of the graph go downwards.

If this is the case, we know that the maximum will be at the vertex.

Here we know that the vertex is:

(50, 1000)

Where remember, x represents the number of items and y represents the profit.

So, given that the maximum is at the vertex, and we know that the vertex is (50, 1000) we can conclude that the maximum profit is $1000, and this happens when the number of produced items is 50.

Then the complete statement is:

"The maximum profit of $1000 dollars is reached when 50 items are produced"

Answer: 22

Step-by-step explanation:

Ok, so the way I do it I multiply then divide.

For Monday I did: ?/220=55/100. what you would do is multiply across then divide by the other number, so 220x55 which is 12100 then you will divide it by 100. So 121 people voted on Monday

For Tuesday: Using the same method. ?/220=45/100 you will multiply 45x220 giving you 9900 then you will divide by 100 giving you 99. 99 people voted on Tuesday.

So to find the DIFFERENCE you need to subtract, so 121-99 leaving you with 22. Also, if you are confused how on where I got 100 from you put the percentage over 100, because percentages go from 0%-100% so you put the partial percentage over the maximum (100)  

The Volume of the right cone (V) that has a diameter of 6 units and a height of 11 units is calculated as: 33π units³.

The volume of a right cone can be determined by applying the following formula:

Volume of a right cone (V) = 1/3 * πr²h, where:

r represents the radius of the right cone

h represents the height of the right cone

Given the following:

radius (r) = 6/2 = 3 units

Height (h) = 11 units

Plug in the values:

Volume of the right cone (V) = 1/3 * π * 3² * 11

= 1/3 * π * 99

= π * 33

Volume of the right cone (V) = 33π units³

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Answer:

167

Step-by-step explanation:

Complete Question:

In the triangles, TR= GE and SR=FE. If GF= 3.2 ft, which is a possible measure of TS?

Answer:

3.2ft

Step-by-step Explanation:

From the given information of the question, we can draft out the diagram of the triangles being depicted here. See attached picture showing triangles RST and EFG.

Since we are told that TR= GE, and SR = FE, it means both triangles are isosceles triangle a having 2 equal sides, and triangles RST and EFG are similar.

Also, given that the measure of the 3rd side (GF) of triangle EFG is 3.2ft, therefore, TS = 3.2ft

Answer:

c

Step-by-step explanation:

Answer:

(4, -4)

Step-by-step explanation:

When something is reflected across the x axis, it's x coordinate turns negative. Same with the y axis.

A sequence of events or things is a number of events or things that come one after another in a particular order. The nth term of

for 6,21,46,81 is 5n²+1.

A sequence of events or things is a number of events or things that come one after another in a particular order.

Write down the nth term of this quadratic number sequence.

6,21,46,81...

number sequence has nth term = an² + bn + c.

Confirm the sequence is quadratic. This is done by finding the second difference.

Sequence =6,21,46,81

1st difference = 15,25,35

2nd difference = 10,10

If you divide the second difference by 2, you will get the value of a.

10/2=5

So the first term of the nth term is 5n².

ext, substitute the number 1 to 4 into 5n².

n=1,2,3,4

5n²=5,20,45,80

Now, take these values (5n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.

5n²+1=6,21,46,81.

Therefore nth term for 6,21,46,81 is 5n²+1.

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Answer:

The maximum profit is achieved when 5 pairs of shoes are sold.

Step-by-step explanation:

To find the maximum profit, we need to find the value of x that maximizes the function P(x). One way to do this is to use calculus.

First, we take the derivative of P(x) with respect to x:

P'(x) = -16x + 80

Then, we set P'(x) equal to zero to find the critical points:

-16x + 80 = 0

Solving for x, we get:

x = 5

Now we need to check if this critical point is a maximum or a minimum. To do this, we take the second derivative of P(x) with respect to x:

P''(x) = -16

Since P''(x) is negative for all values of x, we know that the critical point x = 5 corresponds to a maximum. Therefore, the maximum profit is achieved when 5 pairs of shoes are sold.

Answer:

Irrational

Step-by-step explanation:

The equation that can be used to determine the cost of one drink is 29.18 = 22 + 2x - 5 where the cost of each drink is $6.9

= $22

29.18 = 22 + 2x - 5

29.18 = 17 + 2x

29.18 - 17 = 2x

12.18 = 2x

x = 12.18 / 2

x = 6.9

Therefore, the equation that can be used to determine the cost of one drink is 29.18 = 22 + 2x - 5 where the cost of each drink is $6.9

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Answer:

-8

Step-by-step explanation:

Answer: kindly check attached picture

Step-by-step explanation:

Given the data below :

Juice Mango Orange Apple Pineapple Grapefruit Grape

Proportion of Facings 0.1875 0.250 0.250 0.125 0.125 0.0625

In other to make the proportion of facing visible on the graph we multiply by 100; Hence,

Juice Mango Orange Apple Pineapple Grapefruit Grape

Proportion of Facings 18.75 2.50 2.50 1.25 1.25 6.25

Juice Mango Orange Apple Pineapple Grapefruit Grape

Observed Number of Sales 23 35 46 12 10 5

(a) Construct a single bar chart that contains both the expected proportion of sales based on the proportion of facings and the observed proportion of sales for each type of juice.

Using an online bar chart plotter, the proportion of facings by the blue bars and the red bars depicts the observalues for different type of juice Given.

Hence, from the plot, it could be clearly seen that the distribution of facing is different or not equal to the number of juice sold.

The barchart produced is attached below.

Based on the information given, it should be noted that the single bar chart contains the expected proportion of sales based on the proportion of facings and the observed proportion.

A bar chart simply means a bar graph. It's presents categorical data with rectangular bars that is equal to the values depicted.

From the information provided in the bar chart, it can be seen that the observed proportion for juice, mango, orange, apple, and pineapple is higher than that of the expected proportion.

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Based on the current real and the full employment real GDP, Rayton's economy is at a Recession stage.

The current budget balance in Rayton is -$1,000. The budget can be balanced by reducing government spending or increasing taxes. Both of these would decrease real GDP.

The fact that the current real GDP is less than the full employment GDP shows that the nation is at a recession stage where it is underperforming.

This can be found as:

= Government revenue(taxes) - government spending

= 3,000 - 1,000 - 3,000

= -$4,000

In order to make a balanced budget where government revenue will equal government spending, the government either needs to reduce spending or increase revenue ( taxes ).

Increasing taxes or reducing spending, will lead to less money available for spending in the economy which will lead to a decrease in real GDP.

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(a) Yes, the signal is time-limited because it exists only within the finite duration of 0 to 4.  (b) The Fourier transform of the signal is -8e^(-jω4)/(jω).  (c) No, the signal is not band-limited as its Fourier transform has non-zero values for all frequencies.  (d) The signal f(t) is a compressed and shifted version of g(t) with a time scaling factor of 2 and a time shift of -2. (e) Using the relationship established in (d), the Fourier transform of g(t) can be obtained as -8e^(-jω2)/(jω) without explicitly calculating it from the definition.

(a) To determine if the signal is time-limited, we need to examine its duration. The signal f(t) is defined as -2(t-4) for 0 ≤ t ≤ 4, which means it exists only within this time interval. Since the signal has a finite duration, it is considered time-limited.

(b) To find the Fourier transform of the signal, we can use the Fourier transform properties. The Fourier transform of -2(t-4) is -2e^(-jω4)/(jω), where j is the imaginary unit and ω is the angular frequency. By simplifying this expression, we get -8e^(-jω4)/(jω).

(c) A signal is band-limited if its Fourier transform has non-zero values only within a finite range. From the previous calculation, we can see that the Fourier transform of f(t) is non-zero for all values of ω. Therefore, the signal f(t) is not band-limited.

(d) The signal f(t) and g(t) have a similar form, but g(t) is a time-scaled and time-shifted version of f(t). Specifically, g(t) is obtained from f(t) by multiplying it with e^(-2(2-4)) and restricting its duration to 0 ≤ t ≤ 2. This means g(t) is a compressed and shifted version of f(t).

(e) Using the relationship established in part (d), we can obtain the Fourier transform of g(t) without explicitly calculating it from the definition. By applying the time-scaling property and the time-shifting property of the Fourier transform, we can obtain the Fourier transform of g(t) as -8e^(-jω2)/(jω).

By analyzing the given signal f(t), we determined that it is time-limited but not band-limited. We also explained the relationship between f(t) and g(t), and used that relationship to obtain the Fourier transform of g(t) without directly computing it.

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The percentage change in laptop orders is 83%

Percentage is a measure of frequency. It the fraction of an amount expressed as a number out of hundred. Percentages are represented with the sign %.

In order to determine the percentage change, the first step is to determine the change in laptop leased.

Change in laptops leased = 22 - 12 = 10 laptops

This means that the number of laptops leased increased by 10

The second step is to express the change laptops leased  as a fraction of the laptop leased last year and multiply by 100

10/12 x 100 = 83%

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Answer: 10.2 cm

Step-by-step explanation:

We can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's call the unknown length of the other leg "x". Then we can set up the following equation:

4^2 + x^2 = 11^2

Simplifying this equation, we get:

16 + x^2 = 121

Subtracting 16 from both sides, we get:

x^2 = 105

Taking the square root of both sides, we get:

x = sqrt(105)

x ≈ 10.2 cm (rounded to the nearest tenth)

Therefore, the measure of the other leg is approximately 10.2 cm.

The price of the ticket for a 1400-mile trip when jet fuel costs $6.70 per gallon is $1132.6, and the change in price for the trip from 1400 miles to 1700 miles, with the fuel price staying the same, is $208.5.

a) To find the price of a ticket for a 1400-mile trip when jet fuel costs $6.70 per gallon, we can substitute the values into the function

P(x, y) = 0.5x + 0.03xy + 150.

P(1400, 6.70) = 0.5(1400) + 0.03(1400)(6.70) + 150

P(1400, 6.70) = 700 + 282.6 + 150

            = 1132.6

Therefore, the price of the ticket for a 1400-mile trip when jet fuel costs $6.70 per gallon is $1132.6.

b) To find the change in price if the trip is now 1700 miles but the fuel price stays the same, we need to compare the prices of the two trips.

Let's calculate the price of the ticket for a 1700-mile trip:

P(1700, 6.70) = 0.5(1700) + 0.03(1700)(6.70) + 150

P(1700, 6.70) = 850 + 341.1 + 150

            = 1341.1

To find the change in price, we subtract the price of the 1400-mile trip from the price of the 1700-mile trip:

Change in price = P(1700, 6.70) - P(1400, 6.70)

              = 1341.1 - 1132.6

              = 208.5

Therefore, the change in price for the trip from 1400 miles to 1700 miles, with the fuel price staying the same, is $208.5.

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Answer:

The correct answer is (2,1)

Step-by-step explanation:

The distance, midpoint, and slope  are 4√5 , (2 , 1) , 1/2 respectively.

For any two points A( x₁ , y₁ ) B( x₂, y₂)   the distance, midpoint, and slope  are given by:  1)     \(d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }\)  

                       2)  M(x , y) = { (x₁ + x₂)/2 , (y₁ + y₂)/2 }

                      3)  m= y₂ - y₁ / x₂ - x₁

Given here the points A(-2,-1) and B(6,3)

substituting the values we get,

1) \(d = \sqrt {\left( {-2- 6} \right)^2 + \left( {-1 - 3} \right)^2 }\)    

  \(d = \sqrt {\left( {8 } \right)^2 + \left( {4 } \right)^2 }\)

\(d = \sqrt {\left( 80{ \right)^ }\)

\(d =4\sqrt {\left5 }\)

2)      M(x , y) = { (-2 + 6)/2 , (-1 + 3)/2  }

                     =  (2 , 1)

3)  m = { (6 - (-2) / (3 - (-1)) }

        = 1/2

Hence,  distance, midpoint, and slope  are 4√5 , (2 , 1) , 1/2 respectively.

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